Chapter 5, Problem 5.99P

A rewritable optical disc (DVD) is formed by sandwiching a 15-nm-thick binary compound storage material between two 1-mm-thick polycarbonate sheets. Data are written to the opaque storage medium by irradiating it from below with a relatively high-powered laser beam of diameter $0.4\mu \text{m}$ and power 1mW, resulting in rapid heating of the compound material (the polycarbonate is transparent to the laser irradiation). If the temperature of the storage medium exceeds 900 K, a non-crystalline, amorphous material forms at the heated spot when the laser irradiation is curtailed and the spot is allowed to cool rapidly. The resulting spots of amorphous material have a different reflectivity from the surrounding crystalline material, so they can subsequently be read by irradiating them with a second. low-power laser and detecting the changes in laser radiation transmitted through the entire DVD thickness. Determine the irradiation (write) time needed to raise the storage medium temperature from an initial value of 300K to 1000 K. absorptivity of the storage medium is 0.8. The polycarbonate properties are $\rho =1200{\text{kg/m}}^{\text{3}},k=0.21\text{W/m}\cdot \text{K,}$ and $c_p=1260\text{J/kg}\cdot \text{K}\text{.}$